Question

Dallas, Texas, and Stafford, Texas, are numbered 57 and 58 on the top 100 most diverse cities in the U.S. A random sample of 300 residents from each city were surveyed. The results are listed below.

Dallas (X₁): 202 of 300 surveyed were non-white

Stafford (X₂): 180 of 300 surveyed were non-white

At the 0.01 level of significance, is there enough evidence to conclude that Dallas has a higher proportion of non-white residents than Stafford?

a)Which are the null and alternative hypotheses?

b)What is the test statistic? Round to 2 decimal places

c)What is the p-value? Round to 4 decimal places.

d)Which is the decision?

e)Which the reasoning for the decision?

Answer 1

a)Which are the null and alternative hypotheses?

Null hypothesis

Ho:p1=p2

Alternative hypothesis

Ha:p1>p2

Solution-2:

use ti 83 cal to get test statitsic and p value

p1^=x1/n1=202/300

p2^=x2/n2=180/300

Perform in ti 83 cal:

TESTS>2-PropZtest

enter the data

TI-83 Plus TEXAS INSTRUMENTS 2-PropZTest P1>P2 TEXAS INSTRUMENTS TI-83 Plus EDIT_CALC TESTS 1: Z-Test... 2: T-Test 3:2-SamPZ 4:2-SampTTest.... 5:1-Prop Test.... 382-PropZTest... 7+ZInterval... TANLUU CAFE || ||- 2=1.2674944 P1=.612 t=.6366666667 DTPLOFFSET FROM WINDOW ZOOM CAC TRACE TALE FS GRAPH SDTPLOFFSET FOR WINDOI ZOOM CC RTLEFS TRACE GRAPH QUIT MODE INS DEL QUIT MORE INS DEL

test statistic is

z=1.87

ANSWEr:

1.87

Solution-c:

p=0.0309

Solution-d:

alpha=0.01

p=0.0309

p>0.01

Fail to Reject Null hypothesis

Accept Null hypothesis

Solution-e:

There is no sufficient evidence at 1% level of significance to conclude that  Dallas has a higher proportion of non-white residents than Stafford

TI-83 Plus TEXAS INSTRUMENTS 2-PropZTest P1>P2 TEXAS INSTRUMENTS TI-83 Plus EDIT_CALC TESTS 1: Z-Test... 2: T-Test 3:2-SamPZ 4:2-SampTTest.... 5:1-Prop Test.... 382-PropZTest... 7+ZInterval... TANLUU CAFE || ||- 2=1.2674944 P1=.612 t=.6366666667 DTPLOFFSET FROM WINDOW ZOOM CAC TRACE TALE FS GRAPH SDTPLOFFSET FOR WINDOI ZOOM CC RTLEFS TRACE GRAPH QUIT MODE INS DEL QUIT MORE INS DEL